ABSTRACT
This chapter describes a reliable, appropriate, and efficient wavelet-based technique for the numerical solution of fractional differential equations. It discusses fractional calculus and the numerical solutions for nonlinear fractional differential equations. The chapter considers the analytical and the numerical approach for solving particular nonlinear fractional differential equations like the fractional Burgers–Fisher equation, fractional Fisher's type equation, and time- and space-fractional Fokker–Planck equation (FPE), which have a wide variety of applications in various physical phenomena. These fractional differential equations have proved particularly beneficial in the context of an anomalous diffusion model, a fluid dynamics model, heat conduction, elasticity, and capillary-gravity waves. Fractional calculus is a field of applied mathematics that deals with derivatives and integrals of arbitrary orders. Research and improvements have been made by many others directed to the development of the integral-based Riemann–Liouville fractional integral operator, which has been an essential foundation in fractional calculus ever since. The chapter presents the error analysis for the two-dimensional Haar wavelet method.
